"Infinity is a little bit scary..."

Published: 29 June 2018

World Population Day

Current estimates indicate that roughly 83 million people are being added to the world’s population every year. Even assuming that fertility levels will continue to decline, the global population is expected to reach 8.6 billion in 2030, 9.8 billion in 2050 and 11.2 billion in 2100, according to the medium-variant projection.

These are big numbers and children are often fascinated by them. Ned Rayner is currently a Year 5 pupil. His mum, Rachel Rayner, a Teaching and Learning Adviser (Primary Mathematics), asked him to think about population, numbers and number systems and to write this blog.

Why children like big numbers but find them a little scary

Big numbers look really important compared to little numbers. Lots of people are scared of them but they are just numbers. It is very hard to imagine what they would look like. For example, what would a million smarties look like? Lots of bigger numbers are very hard to say for some people. Don’t be scared it’s just a number just like 3 or 5. The commas in numbers can help to read them, for example in 3,456,789 for the comma to the right say thousand and for the comma to the left say million. So read the number as 3 million, 456 (four hundred and fifty six) thousand and 789.

The worldometers website has some really big population numbers. It’s very cool as you can see the growth of population in the world, how many deaths and births etc. I can’t imagine that many people – I think that many people if all crowded together would take up about the whole state of California. But I don’t think it’s a good idea – it’s hard enough to get 100 people organised for sports day in my school hall!

Why learning about big numbers is now important (versus past)

There are much bigger numbers now – there wasn’t huge numbers in the old days. They only had small amounts of money and people to count because there were fewer people compared to today. Mum’s not that old but she says she remembers buying crisps for 7p. You can’t buy anything for less than 10p now. Because the population is bigger we need more numbers to count them with. Some tribes only needed number words for 1, 2 and 3. Any more was given the word many.

Different counting systems

The different counting systems are interesting because I didn’t know there were so many different ways of counting. Not many people used base ten. In the old days, they may have used base 15 or 20. Some peoples still even use base 3 and base 4 in the same counting system. For example, the Bukaiyip people from Papua New Guinea count in base 3 and 4 depending on what they are counting. Coconuts, days and fish are counted using base-3 and betel nuts, bananas and shields are counted in base-4. It makes my brain ache thinking about that. Mum and I found five different counting systems in Papua New Guinea alone! I think base-10 is easier because I’m used to it.

Why we need zero

If we didn’t have zero, we wouldn’t be able to make larger numbers and you wouldn’t be able to go into negative numbers. In the past many people didn’t like the idea of zero. Zero was invented in India and was made because the circle means never-ending and represents the circle of life. After a while it was used by Arabic scholars. But during the crusades western countries didn’t like zero and didn’t trust Arabic numbers. They were worried that 0 led to negative numbers and this might lead to debt. I think people would still owe money even without zero. So it’s a little hard for me to understand why zero would make that much difference. Mum says we couldn’t have got so far with computers and technology without it. So that’s really amazing that one little circle could be so important.

To infinity and beyond…

Infinity is an endless number that we’ll never be able to find. It is the biggest number ever if it’s even real. We can’t count to it. I’m not even sure if it is a number. Infinity is a little bit scary because no one has ever seen or felt it. It’s hard to imagine. Mum says probably adult mathematicians feel exactly the same as me.

Mum says there are some good books to get children thinking about World Population day, big numbers and counting in different bases. She wrote them here with some ideas. I like the idea of insect counting!

If the World Were a Village by David J. Smith and Shelagh Armstrong
This book imagines the world population in a village of 100 people (allowing pupils to think of percentages. Pupils learn that 22 people would speak Chinese and 17 people wouldn’t be able to read or write. Translated to the whole population 22% of people speak Chinese and 17% cannot read or write. Pupils can investigate population percentages and relate that to the village.

How Big is a Million by Anna Milbourne and Serena Riglietti
This one has a huge poster showing 1 million stars allowing pupils to visualise how extraordinary the quantity 1 million is.

One is a Snail, Ten is a Crab by April Pulley Sayre and Jeffrey Sayre
We count in base ten largely because we have ten digits on our hands. Roman Numerals began this way for example. VI is all of the digits on one hand and 1 more finger for example. But what if we were insect from the book with 6 legs and our counting system was based on that? We might count 1, 2, 3, 4, 5, insect, insect 1, insect 2, insect 3, insect 4, insect 5, 2 insect, 2 insect 1, 2 insect 2 etc. What would 30 be in insect counting? Answer 5 insect. Using the book to suggest how the dog, insect and spider might count, pupils can then investigate counting systems used by different populations around the world such as the ones Ned has mentioned.

Please share any work inspired by World Population Day on Twitter@Hertsmaths or through our Facebook group Herts for Learning: ESSENTIALmaths. We look forward to seeing your pupils' work on really big numbers and number systems.